Aerodynamics and hydrodynamics have much in common because both disciplines involve the study of the movement of a fluid, air or water, past a structure. Surfing, and other water sports such as sailing, power boating, windsurfing, kite surfing, wakeboarding and water skiing, for example, thus share some common aspects derived not only from aerodynamic principles, but also from hydrodynamic principles. This disclosure relates to an invention intended primarily for use on surfboards, but given the teachings of this disclosure is easily practiced in or adaptable to sports involving other watercraft such as those mentioned.
The sport of surfing involves a complex interaction between surfboard, surfboard rider, and waves. As in the sports of skiing and snowboarding, and unlike other board-riding sports such as windsurfing, kite surfing, water skiing, and water boarding, surfers while surfing are propelled by the effects of gravity pulling the surfer down wave faces. Unlike other board sports, surfers after riding a wave toward shore typically must propel themselves back to the spot where they can catch the next wave.
Surfing requires more than simply sliding uncontrolled down a wave face; good surfers are able to control both surfboard speed and surfboard direction. Similarly, good surfboards are those that are capable of high speeds if the surfer so desires, are otherwise easily maneuverable, are easy to paddle, and are quick to catch waves. Surfboard speed and maneuverability depend on a variety of characteristics of the surfboard itself, and of attached surfboard appendages, known as fins, although some people have referred to surfboard fins as skegs. Modern surfboards uniformly use one, two, three, or four fins, but most commonly either one large center fin, or one large center fin, and two side fins as shown in FIGS. 5, 6, 10, and 11. In this section, the term “surfboard” is meant to include the attached fins, unless otherwise indicated.
Within certain limits, surfboard speed typically is accomplished by adjusting the pitch of the board in relationship to the wave face. Pitch is the longitudinal angle the surfboard makes from the horizontal. Surfboard pitch is controlled by the surfer moving forward toward the nose of the board, or backward toward the tail of the board, and thus adjusting the center of gravity of the surfer and surfboard system in relation to the center of buoyancy such that the board slide down the wave face with the correct inclination such that it either planes on the water or stalls in the water, to speed up or to slow down the board. Generally speaking and to certain limits, surfboard speed is increased by moving forward on the board and decreased by moving backward on the board. All else being equal, a surfboard—including its fins—with less drag will move faster through the water because drag is the force of resistance to forward motion. Thus with less resistance, a board with less drag can move faster through the water. Surfboard speed is thus is inversely related to the surfboard's drag.
Likewise, surfboards are easier to paddle where they have less drag, again because drag is the force of resistance to the surfboard's forward motion. Thus a surfer paddling a surfboard that has less drag can do so more easily and for a longer period of time before exhaustion.
Surfboards typically cannot catch waves by lying idle in the surf. Rather, the surfer at the lineup must await the approach of a suitable wave, then turn to the wave's direction of travel, and quickly accelerate by paddling to an appropriate velocity to catch the coming wave. Surfboards that have less drag will catch more waves more easily because the surfer can expend less energy to accelerate the board to wave-catching velocity, or can accelerate more quickly. Paddling, wave-catching and maneuverability also are better on surfboards with less drag. Surfboard acceleration is this inversely related to the surfboard's drag.
Drag is a function of the surfboard's shape, surface area, attitude in the water, and shape, as well as a function of the design of the surfboard fins. Minimizing surfboard drag and surfboard-fin drag is particularly important because unlike other ski or board sports, after surfers have successfully ridden a wave, they must propel themselves by paddling back through the surf, or back to the lineup to catch another wave, which is increasingly tiresome or exhausting with increasing drag. In order to catch waves, drag is likewise important to keep that a minimum so that surfers may paddle quickly to catch the wave, something that is increasingly difficult to do with increasing drag. Decreased drag thus enables surfers to surf longer and to catch more waves.
Turning of a surfboard involves a complex interaction between a surfer adjusting the roll angle of the board, by adjusting the pitch of the board, and by surfboard and surfboard-fin design. Generally speaking, surfboards having more rocker, the curved shape of a banana with surfboard tip and tail elevated from the horizontal, have a natural tendency when placed on edge to turn consistent with the rocker shape. But increased rocker also increases drag, compromising speed, compromising the ability to accelerate to catch waves, and increasing the difficulty of paddling the surfboard. Surfboard edges, or rails, can be anything from circular or rounded in shape, known as soft rails, to flat or hard rails in which the flat surfboard bottom turns sharply upwardly to meet the surfboard's top deck. Surfboards with hard edges tend to turn more quickly or more sharply than those with softer rails. Surfboards, as opposed to surfboard fins, have undergone a significant and largely empirical design evolution applying these concepts since the beginning of the modern sport in approximately the 1950s and 1960s.
But surfboard-fin design has evolved relatively little over the past several decades of the modern sport of surfing. Surfboard fins assist turning of a surfboard much as rudders and ailerons help boats or airplanes turn or maneuver, by providing largely lateral resistance and lift, with some vertical lift component depending on the orientation to the vertical of the fin in the water. Without fins, a surfboard in a turning maneuver would tend to spin out, whereas with one or more fins, a surfboard rider can use his or her weight to control the yaw angle of the fin while riding a wave, and can use the attached fin or fins as a lever against which to turn the board. As in surfboard design, minimizing drag in designing fins is an important objective because doing so increases speed, increases acceleration capabilities, and minimizes necessary paddling effort.
But minimizing drag of the fins is not enough; else the fins could of course be infinitesimally small to the point of nonexistence. To the contrary, surfboard-fin design must minimize drag while maximizing lift, because lift is the force that makes the surfboard turn, just as the force of lift allows sailboats to sail toward the wind, airplanes to fly, and both to turn. Thus a more efficient, higher-lift fin can be smaller in size, with less surface area, and thus with less drag than a less-efficient fin that has more surface area and more drag.
Surfboard fins available on the market today, and for which patent applications have in the past been made or granted almost uniformly ignore important hydrodynamics principles, or applicable aerodynamics principles.
Hydrodynamics teaches that interference drag is caused by the intersection of a watercraft the hull and appended to such as a keel. Designers have attempted to minimize interference drag by shortening the length of the keel-to-hull intersection by means of a cut away at the trailing edge of the keel. Although helpful, the cut away trailing edge tends to be less effective at reducing interference drag than a forwardly upwardly protecting root after leading edge.
Hydrodynamics and aerodynamics teach that lower sweepback angle increases lift while decreasing drag for a given surface area. But foil selection is critical because lower sweepback-angle fins are more prone to stalling than higher sweepback-angle fins. Greater sweepback angle on a fin that is being turned places the entire planform obliquely to the turning direction and functions more as a brake than a higher-aspect ratio fin.
Hydrodynamics and aerodynamics teach that higher-aspect ratio planforms generate more lift with less drag than lower aspect ratios. Aspect ratios of 2:1 or more are preferred over lower aspect ratios.
Hydrodynamics teaches that underwater foils should not be too thin, or cavitation will occur. Underwater foils should be between 9 percent and a 15 percent thickness.
Hydrodynamics teaches that fins used as rudders should not be too thin, and that a certain foil sections maintain laminar flow necessary to produce lift with a minimum drag over a wide variety of angles of attack as contrasted with other types of foil sections. NACA 0010 and 0012 foil sections have a demonstrated history of effectiveness. Maximum foil width should be no greater than 35% aft of the leading edge, and point of maximum width 30 half of the leading edge is demonstrated as being particularly desirable for rudders as in NACA 0010 and 0012 series foils.
Hydrodynamics teaches that the end of fins should have the same shape as the cross-section of the foil shape within the fin itself.
Hydrodynamics teaches that foils should not have a great taper ratio and that the tip chord length should be between 40 and 60 percent of the root chord length.
Aerodynamics and hydrodynamics teach that endplates, fences, wings, or winglets placed at the end of wings, keels, or other hydrofoils can be effective at reducing the loss of lift that occurs at the end of such surfaces due to downwash and tip-vortex drag. But if improperly designed, used, or placed, such devices will increase surface area to such an extent that overall drag is increased, and there is no net benefit demonstrated by the use of such endplates, fences, wings, or winglets.
Aerodynamics and hydrodynamics teach that winglets, as opposed to endplates, fences, or wings, have proven effective at reducing induced drag while increasing lift in greater proportion than the increased area and associated additional form drag of the winglet, and thus greater lift with less drag than an equivalent increase in planform area or span length. Winglets have a shorter chord length than the wing tips to which the winglets are attached, as distinguished from endplates, fences, or wings. Winglets should themselves be effective lifting surfaces, and should be designed with the aerodynamic and hydrodynamics principles discussed above.
Aerodynamics and hydrodynamics teach that elliptical wings or fins yields tip vortices that are less concentrated at the tips, the downwash is spread more evenly across the wingspan. Here, the term “elliptical” does not necessarily refer to the shape of the planform, which planforms generally do exhibit elliptical lift, but to the distribution of lift across the planform. Rectangular wings or fins can yield a close approximation to elliptical lift distribution.
Aerodynamics and hydrodynamics teach that winglets themselves can benefit from winglets, which when attached to winglets on a wing or fin, result in a C-shaped wing or fin shape to the wing or fin to which the winglets are applied when viewed from the leading or trailing edges of the wing or fin assembly. Overall wing or fin lift is increased with such a C-shaped wing or fin assembly.
Existing surfboard fins typically do not incorporate the aerodynamic and hydrodynamic principles discussed above. For example, surfboard fins typically are heavily raked or swept back from the vertical, often to the point where the leading edge of the surfboard fin is approximately 35 degrees to the perpendicular to the fin root chord. This condition encourages downwash, the situation in which water flowing horizontally past the fin moves from one side of the fin to the other, then creates a large vortex behind the fin as it travels though the water. Moreover, the high-sweepback angle contributes to the loss of the laminar flow of water past the fin, such that the water on the back half of the fin is turbulent as opposed to smoothly flowing, and thus such fins stall earlier and lose lift and turning ability at a shallower angle of attack than a fin of low sweepback angle. Turbulent conditions as encountered with typical surfboard fins should be avoided in order to minimize drag while maximizing lift.
Surfboard fins typically have no recognizable hydrodynamic section or foil shape; they appear to not be designed or engineered other than to look good, and they look like one another. Indeed, many surfboard fins are nearly flat in section, particularly when used as side fins. When a surfboard with such flat-sectioned fins turn or yaw such that the angle of attack between fin and moving water no longer is straight ahead, or a zero angle of attack, many surfboard fins quickly stall. Stalling is the critical loss of foil lift, the angle of attack at which fins cease functioning as fins, and begin working only as brakes, creating drag but no lift. In airplanes, the airplane dropping from the sky illustrates wing stalling, whereas in surfing, fin stalling generally results in the board slowing or stopping, and in losing the wave, which continues uninterrupted. Consequently, a shortcoming of existing surfboard-fin design is that they are typically too flat in section, and are not engineered to incorporate low-drag foil sections that produce lift with minimum drag over wide range of yaw angles.
Surfboards today commonly have one, two, three, or four fins, but combinations of one fin and three fins are most common. When in combinations of more than one fin, the side fins typically are arranged near to the edges, or rails of the board. Side fins typically today are toed-in, arranged not parallel to the longitudinal axis of the surfboard, but rather with their leading edges pointed inwardly by a few degrees. Although this arrangement assists the turning of the board when only one such fin is immersed, when two such toed-in fins are immersed, they act together as a brake, increasing drag, because one wants to turn left, while the other right. Toed-in side fins is simply an effort to work around, accommodate, or to resolve existing fins' inability to create lift over a wide range of yaw angles without stalling, or to accommodate flat-sided side fins, but in the process, the typical arrangement of side fins increases drag and promotes stalling as compared to a non-toed-in arrangement of side fins. Moreover, the toed-in arrangement of side fins inhibits paddling and acceleration, causing earlier surfer exhaustion, and inhibiting acceleration and thus wave-catching ability.
With some exceptions, surfboard fins generally have a much longer chord length at their base, the fin root, than they have at their tips, thus a high taper ratio, and typically fins have a short span, and a low aspect ratio. Although this design combination assists with strengthening the fin, it aggravates drag. Hydrodynamics principles teach that underwater appendages such as keels and rudders, or analogously, surfboard fins, should have high aspect ratios and comparatively short root lengths and taper rations between 0.4 and 0.6 in order to maximize lift while minimizing drag.
Some surfboard fins, as in some old sailboat keel designs, decrease the fin root length by means of a cutaway or a scallop where the fin meets the board at the fin's trailing edge. But hydrodynamic principles teach that a cutaway at the trailing edge, while helpful to decreasing drag, is less effective at minimizing drag than a forward-projecting, foil-shaped blended keel or fin section, much like bulbs on the bows of freighters and the other ocean-going ships actually decrease drag by projecting forward of the ship's hull.
Aerodynamics and hydrodynamics principles teach that an endplate, wing or winglet, a surface oriented generally perpendicular to the fin and parallel to the path of water travel past the fin, decreases or prevents drag-inducing and lift-decreasing downwash. Downwash is the tendency of a fluid on the high-pressure side of a wing, keel, or fin to move to the low pressure side, in a circular motion. Plates or wings are effective at preventing that movement from one side of the wing, keel, or fin, but at a penalty—the plate or wing adds surface area to the wing, keel or fin. Hydrodynamics studies and experiments, however, teach that winglets—small wings with chords significantly shorter than the fin chord itself and with significantly smaller areas that the wing, keel or fin to which attached—produce the same or similar downwash-canceling effects as wings, but with a much smaller surface area, and thus with a much smaller drag penalty. Thus the incorporation of winglets, as opposed to wings, increases lift while decreasing drag.
Moreover, winglets assist in maintaining lateral lift that otherwise would be lost when a surfer rolls the board to one side in a turning maneuver thus placing the surfboard fin at an angle to the vertical, shortening the vertical length, and creating a tendency of the fin to pop out of the water, losing all turning control of the fin. To be effective and to avoid increasing drag, the winglets themselves must be effective lift-producing surfaces, must be correctly sized and placed or they risk increasing drag by virtue of their added surface area. Increasing lift with low drag increases wing, keel, and fin efficiency and speed.
Hydrodynamics teaches that a rounded nose section, as exists with NACA 0010 and 0012 foil sections, is better for rudder design because such rounded nose sections facilitate lift production over a wide range of yaw angles. Existing fin design typically are sharp or angular at the nose. In addition to decreasing the effective useful range of fin before stalling, the design is dangerous when it strikes surfers, because of the sharp surfaces, especially the tip.
Surfers, especially those who surf longer surfboards or surfboard called longboards, often attempt to noseride, a stance on the board forward of the board's midsection, as shown in FIG. 11. Surfboards are prone to nosediving when a surfer is surfing a surfboard from that location.
The following definition list is helpful to an understanding of this disclosure.
TermDefinitionAngle of attackThe angle between the direction of finmovement through the water and thefin's chord line.Aspect ratioAspect ratio is a measure of how longand slender a fin is from fin root to tip.The aspect ratio of the fin is defined asthe square of the span divided by the finarea. Typically high-aspect-ratio finshave long spans and aspect ratios of 2:1or greater, while low-aspect-ratio finshave short spans and lower aspectratios. Higher aspect-ratio fins havelower drag and higher lift than loweraspect-ratio fins.Boundary layerThe layer of water molecules near thesurface of the fin whose velocities arechanged that by movement of the finthrough the water. Boundary layer flowmay be either laminar or turbulent.ChordThe distance between the leading edgeof the fin and the fin's trailing edge.Chord lineThe line between the fin's leading andtrailing edges.DownwashA fin with an angle of attack other thanzero creates lift and has a difference inwater pressure on the two sides of thefin. Near the fin tip, water is free tomove from the region of high pressureto the region of low pressure, creating acircular water flow from one side to theother, which creates a vortex or helixbecause of the fin's movement throughthe water. Larger circular flows result inlarger vortices, greater drag, and lift.The presence of winglets at or near thetip of the fin inhibits this circular flow,reduces vortex size, decreases drag andincreases lift.DragDrag is the hydrodynamic force thatopposes any watercraft's motion throughthe water, and is a vector quantity alongand opposed to the watercraft's path oftravel through the water. Drag isdirectly proportional to the area of thefin, and also is affected by fin shape, foilshape, fin thickness, and fin aspect ratio.Fin rootThat portion of the fin that constitutesthe base of the fin when the fin is withinthe fin box, the lowest exposed portionof the fin when in use.Fin baseThe portion of the fin intended to fitsnugly with a fin box to limit unintendedmovement, while providing a means ofadjustability in the longitudinal direction.Fin boxThe channel within into which the finbase is placed, typically with a channelthat allows longitudinal adjustment,while restricting side-to-side movement.The fin box is not claimed as aninvention in this disclosure.FoilThe cross-sectional profile shape of thefin.Laminar flowLayered or smooth-flowing water withinthe boundary layer, as opposed toturbulent or disordered flow within theboundary layer.LiftThe vector-quantity force created by themovement or turning of water past acurved fin surface, which force actsperpendicular to the direction of waterflow. Lift is directly proportional to thearea of the fin.LineupThe spot outside the area of breakingsurf at which surfers await waves to ride.The takeoff zone from which surfersmust quickly accelerate from a standstillto a sufficient velocity in order to catchthe approaching wave.NACAThe National Advisory Committee onAeronautics, the predecessor to NASA.NACA performed extensive testing onairfoil shapes to determine the lift anddrag characteristics of various foilshapes.PitchPitch is the angle of deviation from thehorizontal of the surfboard's or otherwatersports board's longitudinal axis-e.g, the nose of the board or watercraftis pointed somewhat upwardly ordownwardly, as in airplanes when theytake off and climb or descend.PlanformThe planar shape of the wing or foil,which for wings is typically the outline ofthe horizontal plane, and for ruddersand fins, the outline of the vertical plane.RollRoll is the angle of deviation from thehorizontal of the surfboard's or otherwatersports board's side-to-side axis-e.g. the board is leaning somewhat onits right or on its left edge, as inairplanes when they bank their turns.StallLoss of lift, as demonstrated by theturbulent flow of water past the fin.Differently shaped foils have differentpoints or angles of attack at which theystall. A stalled fin moving through thewater loses lift, but increases drag, thusacting as a brake.SweepbackThe angle by which the one-quarter-chord line of the foil sections within theplanform deviates from theperpendicular to the root chord. Someauthorities refer to leading edgesweepback angle, which as the nameimplies refers to the angle away from theroot chord perpendicular of the wing orfin's leading edge.Water sports boardA watercraft primarily used by a singlerider, propelled by gravity, waves, windor by towing, such as a surfboard, akite-surfing board, a sailboard orwindsurfer, a waterski, or a wakeboard.WingletA planar, foil-sectioned projectionsubstantially perpendicular to the finplane, generally placed at or near a fintip or wingtip to reduce tip vortices andconsequent downwash and drag.YawThe angle of deviation from straightforward in the path of travel to anorientation other than straight, aspinning about the vertical axis, as inairplanes landing in a strong crosswindthat “crab” their way to a safe landing.Rudders that steer move though anangle of yaw, as do fins on a turningsurfboard.